1168 



The quantity A is a constant; its value results from the equation 



~ Vd<T, dr ÖT do J dq V 



)dq [^dgdr drdqjda,' ^^^^ 



In (13) and (14) the quantities (j,^y,^,^^,R,,r,y^ are to be considered 

 as functions of q,(yo,r,'*^. 



da 

 In (14) the difference factored by — can be represented by a power 



series in fi without constant term ; the same is the case with 

 — , only here also the first power of (i fails. Thus: 



di> dd d«j bo \b(i 



- — ^ ^ r — I — m ƒ!* > pon-er series m [x. 



0(7, Ox or oo,J Oq 



Considering the fact that A is constant and developing the 



da 

 difference factoi'ed bv ;;;— , we get: 

 " oa. 



A = 



Oq ox Ot oq or Oq _ 



^ -\- fi' )■ power series inn. 



Thus 



A=r 



dg, do, ^ dg^ dO, 

 dr dq Ot dq 



- 4" ft* X power series in f.r, 



in the derivatives occurring in this formula, the quantities o, ,(>,/>*» 

 are to be considered functions of g^, <'i^,q and t. 



Putting R,=:(i^F,, from the system of equations (A) of Chapter 

 II, ^ 3, of the "Investigations" we deduce: 



dc., d^F, d^F, 



If T 



As 



/r 



' dr dt>ö6'''' ' d<9' 

 dg. 



, then (), = 8, = 0, thus 



ÖT ,_ 



dg. 



we get : 



putting 



dr rd'R, 



1 ö«^„ 



=r 1', 



' di 



= 0. 



48 dr» ' 



4- f^* X power series in fi ; 



2 



